chore(i8n,learn): processed translations

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2021-02-06 04:42:36 +00:00
committed by Mrugesh Mohapatra
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---
id: 5900f3b11000cf542c50fec4
title: 问题69大欧拉
title: 'Problem 69: Totient maximum'
challengeType: 5
videoUrl: ''
forumTopicId: 302181
dashedName: problem-69-totient-maximum
---
# --description--
EulerTotient函数φn\[有时称为phi函数]用于确定小于n的数字的数量这些数字是n的相对素数。例如1,2,4,5,7和8都小于9且相对于9φ9= 6。
Euler's Totient function, φ(`n`) \[sometimes called the phi function], is used to determine the number of numbers less than `n` which are relatively prime to `n`. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)=6.
n相对素数φnn /φn2 1 1 2 3 1,2 2 1.5 4 1,3 2 2 5 1,2,3,4 4 1.25 6 1,5 2 3 7 1,2 3,4,5,6 6 1.1666 ... 8 1,3,5,7 4 2 9 1,2,4,5,7,8 6 1.5 10 1,3,7,9 4 2.5
<div style='margin-left: 4em;'>
可以看出对于n≤10n = 6产生最大n /φn。找到n≤1,000,000的值其中n /φn是最大值。
| !!crwdBlockTags_15_sgaTkcolBdwrc!! | Relatively Prime | φ(!!crwdBlockTags_16_sgaTkcolBdwrc!!) |!!crwdBlockTags_17_sgaTkcolBdwrc!!/φ(!!crwdBlockTags_18_sgaTkcolBdwrc!!) |
| ------------ | ---------------- | --------------- | ---------------------------- |
| 2 | 1 | 1 | 2 |
| 3 | 1,2 | 2 | 1.5 |
| 4 | 1,3 | 2 | 2 |
| 5 | 1,2,3,4 | 4 | 1.25 |
| 6 | 1,5 | 2 | 3 |
| 7 | 1,2,3,4,5,6 | 6 | 1.1666... |
| 8 | 1,3,5,7 | 4 | 2 |
| 9 | 1,2,4,5,7,8 | 6 | 1.5 |
| 10 | 1,3,7,9 | 4 | 2.5 |
</div>
It can be seen that `n`=6 produces a maximum `n`/φ(`n`) for `n` ≤ 10.
Find the value of `n` ≤ 1,000,000 for which n/φ(`n`) is a maximum.
# --hints--
`euler69()`应该返回510510。
`totientMaximum()` should return a number.
```js
assert.strictEqual(euler69(), 510510);
assert(typeof totientMaximum() === 'number');
```
`totientMaximum()` should return 510510.
```js
assert.strictEqual(totientMaximum(), 510510);
```
# --seed--